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A149948
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Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, -1, 1), (0, 1, -1), (1, 0, 0), (1, 0, 1)}
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0
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1, 2, 5, 15, 50, 174, 641, 2437, 9431, 37579, 152175, 621880, 2586180, 10863494, 45888641, 196085764, 843672956, 3643784480, 15865824267, 69430498992, 304679850430, 1345095584340, 5961023042885, 26473680550898, 118118544559256, 528599197303464, 2369585532646061, 10661241970191969
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
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MATHEMATICA
| aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]
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CROSSREFS
| Sequence in context: A149945 A149946 A149947 * A093129 A020876 A149949
Adjacent sequences: A149945 A149946 A149947 * A149949 A149950 A149951
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KEYWORD
| nonn,walk
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AUTHOR
| Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
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